Agradecimentos: The research leading to this article has been funded by the São Paulo Research Foundation (Fapesp) through grants 2012/17948-4, 2013/23085-1, 2015/00209-2 and 2013/08293-7 (CEPID). Support from CAPES and CNPQ has been fundamental to the development of the present research. This is gratefully acknowledged Ver menos

This work presents a detailed description of the formulation and implementation of the Atomistic Finite Element Method AFEM, exemplified in the analysis of one- and two-dimensional atomic domains governed by the Lennard Jones interatomic potential. The methodology to synthesize element stiffness matrices and load vectors, the potential energy modification of the atomistic finite elements (AFE) to account for boundary edge effects, the inclusion of boundary conditions is carefully described. The conceptual relation between the cut-off radius of interatomic potentials and the number of nodes in the AFE is addressed and exemplified for the 1D case. For the 1D case elements with 3, 5 and 7 nodes were addressed. The AFEM has been used to describe the mechanical behavior of one-dimensional atomic arrays as well as two-dimensional lattices of atoms. The examples also included the analysis of pristine domains, as well as domains with missing atoms, defects, or vacancies. Results are compared with classical molecular dynamic simulations (MD) performed using a commercial package. The results have been very encouraging in terms of accuracy and in the computational effort necessary to execute both methodologies, AFEM and MD. The methodology can be expanded to model any domain described by an interatomic energy potential Ver menos